In this paper we develop several mathematical models of Allee effects. We start by defining the Allee effect as a phenomenon in which individual fitness increases with increasing density. Based on this biological assumption, we develop several fitness functions that produce corresponding models with Allee effects. In particular, a rational fitness function yields a new mathematical model that is our focus of study. Then we study the dynamics of 2-periodic systems with Allee effects and show the existence of an asymptotically stable 2-periodic carrying capacity.
Document Object Identifier (DOI)
Elaydi, S. N., & Sacker, R. J. (2010). Population models with Allee effect: a new model. Journal of Biological Dynamics, 4, 397-408. doi: 10.1080/17513750903377434
Journal of Biological Dynamics